Current source rectifier modulation in discontinuous modes of operation

ABSTRACT

Systems and methods disclosed herein include a controller for a current source rectifier that is configured to facilitate operation in both continuous and discontinuous conduction modes. The controller comprises a discontinuous mode detection unit configured to determine when input current of the current source rectifier becomes discontinuous and a duty cycle calculation unit adapted to calculate duty cycles for the current source rectifier differently for operation in continuous or discontinuous mode. The controller is adapted to transition to a mode of operation to provide an input current that approximates a sinusoidal current during both the continuous and discontinuous modes of operation. The controller outputs control signals to turn on one or more of the electrical switches in the current source rectifier based on the calculated duty cycles.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/821,604, filed May 9, 2013, entitled “CURRENT SOURCE RECTIFIERMODULATION IN DISCONTINUOUS MODES OF OPERATION,” the disclosure of whichis hereby incorporated by reference in its entirety for all purposes.

FIELD OF THE INVENTION

The embodiments described herein relate generally to current sourcerectifiers. More particularly, the embodiments described herein relateto a method of modulating a current source rectifier in discontinuousmodes of operation. Merely by way of example, the embodiments describedherein include dead-beat current injection modulation of a currentsource rectifier in both continuous and discontinuous modes ofoperation. These and other embodiments along with many of theiradvantages and features are described in more detail in conjunction withthe description below and corresponding figures.

BACKGROUND OF THE INVENTION

Conventional current source rectifiers assume operation in continuousmode where current flows through the direct current (“DC”) link inductorof the current source rectifier. In order to maintain continuousconduction of current through such a DC link inductor, either a largeinductor has to be used, which negatively affects the size and powerdensity of the current source rectifier, or the input current has to bemaintained at a sufficiently high switching frequency, which negativelyaffects the efficiency of the current source rectifier. For this reason,voltage source rectifiers have been preferred over current sourcerectifiers for many applications that require small size or lowerswitching frequencies. However, voltage source rectifiers experiencenumerous problems that cause unwanted distortion on and conductedelectromagnetic emissions into the input voltage and current sources.These problems can be mitigated using additional input filteringhardware, but this leads to additional size and thus even lower powerdensity.

The current source rectifier is an attractive alternative to the voltagesource rectifier, more widely used by industry, because it can achieveAC-to-DC voltage conversion with nearly sinusoidal input currents withless input filter components as well as with a smaller overall size.Current source rectifiers depend upon a continuous DC link current inorder to convert alternating current (“AC”) input voltages to DC outputvoltages. That is, conventional current source rectifiers are built uponthe assumption that the DC link current, such as i_(p) shown in FIG. 1A,does not fall below zero during operation.

This is accomplished by keeping the inductance value or the inputswitching frequency and the average load current at sufficiently highvalues such that i_(p) appears as a constant current source. Theswitching frequency and inductance are also typically selected such thatthe voltage ripple on i_(p) is less than 10% of its rated value. But ata sufficiently light load values, the current source rectifier willenter discontinuous conduction mode of operation. The load at whichdiscontinuous mode occurs will be more significant and more prevalent asthe size of the DC link inductor L_(p) is reduced to improve powerdensity or when the switching frequency is reduced to improveefficiency. Thus, conventional current source rectifiers simply attemptto avoid discontinuous operation by increasing the size of the DC linkinductor L_(p) (thus reducing power density) or increasing the inputswitching frequency (thus reducing efficiency); or by adding additionalhardware, such as dynamic braking, in order to avoid discontinuousoperation altogether. These measures often make the current sourcerectifier an unattractive alternative for many applications.

FIG. 1A depicts an example block diagram of a conventional controllerfor a current source rectifier according to the prior art. The currentsource rectifier 110 shown in FIG. 1A is an active AC-to-DC rectifierthat converts three-phase AC input power to a controlled DC voltagethrough an active rectification process and drives a constant power load104. In the illustration, the three-phase AC input power is shown comingoff of an AC power grid 102 and is provided to the current sourcerectifier 110 through input lines a, b, and c. A conventional controller101 receives the input voltages via signal drivers 106 and 108. Theconventional controller 101 also receives output voltage v_(o) as wellas the DC link current i_(p) through the inductor L_(P) from the currentsource rectifier 110. Controller 101 then provides control signalsU_(i1)-U_(i6) to control the switches S_(i1)-S_(i6) of the currentsource rectifier 110, respectively.

FIG. 1B depicts an example block diagram of some of the main componentsof a conventional controller for a current source rectifier. As shown,conventional controller 101 includes feed-forward controls 120 andfeedback controls 124. These units receive the output voltage v_(o) aswell as user selection of a desired output voltage v_(o)*. The feedbackcontrols 124 provide the modulation index m_(i) to the duty cyclecalculation unit 130. The duty cycle calculation unit 130 also receivesthe phase value φ of the three-phase input power and calculates the dutycycles d_(k) _(—) CCM and d_(n) _(—) CCM based on those values. Thecalculated duty cycles control the signal pulses d_(k) that are providedto the current source rectifier to control the switches S_(i1)-S_(i6) ofthe current source rectifier.

As used herein, the acronym “CCM” stands for “continuous conductionmode” and represents the fact that, for conventional current sourcerectifiers, it is assumed that the current through the DC link inductoris continuous during operation. When discontinuous conduction mode(“DCM”) occurs in a conventional current source rectifier, the resultantinput currents exhibit low order harmonic distortion and a voltageboosting effect occurs on the output such that the output voltage of thecurrent source rectifier is difficult to control. Even worse, whendiscontinuous conduction occurs in conventional current sourcerectifiers, it can also cause voltage stresses to occur on powersemiconductor devices that can cause damage. These phenomena aregraphically demonstrated in FIG. 2, which depicts example graphs showingcharacteristics of a conventional current source rectifier duringdiscontinuous conduction mode of operation. The output voltage graph 201demonstrates a loss of control of the output voltage v_(o). At startup,the output voltage v_(o) far exceeds the user-selected output voltagev_(o)*. Further, the input current graphs 204 demonstrate highdistortion on the average input current <i_(k)>, which is shown by theclipping pattern where the input signal should be substantiallysinusoidal. The input currents are referred to herein generally as<i_(k)> and <i_(n)>, which represent the input current on any two of thethree input phases i_(a), i_(b) or i_(c). These undesirable side-effectsare caused during discontinuous conduction mode when at least part ofthe DC link current i_(p) falls below zero as shown in graphs 206.

These undesirable side-effects are usually mitigated by dissipativecircuitry to keep the current source rectifier from going too deeplyinto discontinuous conduction mode. Unfortunately this further increasesthe size of the circuit and reduces efficiency. Emerging low powerapplications (e.g., <10 kW) use Silicon Carbide (“SiC”) metal-oxidesemiconductor field-effect transistors (“MOSFETs”) in current sourcerectifiers in order to allow very high switching frequency andreasonable efficiency. But SiC MOSFETs are expensive and have limitedavailability in size and range.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A depicts an example block diagram of a conventional controllerfor a current source rectifier.

FIG. 1B depicts an example block diagram of the components of aconventional controller for a current source rectifier.

FIG. 2 depicts example graphs showing characteristics of a conventionalcurrent source rectifier during discontinuous conduction mode ofoperation.

FIG. 3A depicts an example block diagram of a controller for a currentsource rectifier according to one embodiment.

FIG. 3B depicts an example block diagram of a discontinuous modedetection unit of a controller for a current source rectifier accordingto one embodiment.

FIG. 3C depicts a graph demonstrating h_(k), h_(n), i_(p), and <i_(p)>for the current source rectifier operating in CCM according to oneembodiment.

FIG. 4 depicts an example of a current source rectifier in a firstswitch state according to one embodiment.

FIG. 5 depicts an example of a current source rectifier in a secondswitch state according to one embodiment.

FIG. 6 depicts an example of a current source rectifier in a thirdswitch state according to one embodiment.

FIG. 7 depicts an example representation of a phasor diagram for usewith certain embodiments.

FIG. 8 depicts an example graph of input-to-output voltage ratios of thecurrent source rectifier according to one embodiment.

FIG. 9 depicts example graphs of the DC link current of the currentsource rectifier during symmetrical and asymmetrical discontinuous modeoperation according to one embodiment.

FIG. 10 depicts an example flow chart of a process for controlling acurrent source rectifier according to one embodiment.

FIG. 11 depicts an example graph of input currents for the currentsource rectifier during discontinuous conduction mode according to oneembodiment.

SUMMARY OF THE DESCRIPTION

The embodiments described herein relate generally to current sourcerectifiers. More particularly, the embodiments described herein relateto a method of modulating a current source rectifier duringdiscontinuous modes of operation. Merely by way of example, theembodiments described herein include dead-beat current injectionmodulation techniques for current source rectifiers in discontinuousmodes of operation.

Systems, apparatuses, and methods disclosed herein include a controllerfor a current source rectifier that is adapted to transition betweencontinuous and discontinuous modes of operation in order to provide aninput current that approximates a sinusoidal input current during bothmodes of operation. The controller includes a discontinuous modedetection unit configured to detect when the DC link current of thecurrent source rectifier becomes discontinuous and a duty cyclecalculation unit adapted to calculate duty cycles for the current sourcerectifier differently for operation in continuous or discontinuous mode.The controller is adapted to output control signals to turn on one ormore of the electrical switches in the current source rectifier based onthe calculated duty cycles.

Numerous advantages are achieved by way of the techniques describedherein over conventional techniques. Embodiments are adapted to detectwhether a current source rectifier is in CCM or DCM, and then to switchbetween different calculations of duty cycle accordingly. For example,embodiments provide revised calculations for the duty cycles associatedwith active electrical switches of a current source rectifier that willensure the filtered or time-averaged three-phase input currents arenearly sinusoidal and the input-to-output voltage ratio is linear.

These and other embodiments, along with many of their advantages andfeatures, are described in more detail in conjunction with thedescription below and corresponding figures.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

Throughout this description for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the present invention. It will be apparent, however, toone skilled in the art that the present invention may be practicedwithout some of these specific details. In other instances, well-knownstructures and devices are shown in block diagram form to avoidobscuring the underlying principles of the described embodiments.

The systems and methods introduced herein are adapted to provide acontroller for a current source rectifier that is adapted to transitionbetween the continuous and discontinuous modes of operation in order toprovide an input current that approximates a sinusoidal input currentduring both modes of operation. The controller includes a discontinuousmode detection unit configured to detect when the DC link current of thecurrent source rectifier becomes discontinuous and a duty cyclecalculation unit adapted to calculate duty cycles for the current sourcerectifier differently for operation in continuous or discontinuous mode.The controller is adapted to output control signals to turn on one ormore of the electrical switches in the current source rectifier based onthe calculated duty cycles. At least certain embodiments of thecontroller provide what is known as Dead-Beat Current Injection (“DBCI”)techniques for pulse-width modulation (“PWM”) of the current sourcerectifier that will ensure nearly sinusoidal input current and linearinput-to-output voltage control during discontinuous or continuousconduction modes of operation. These embodiments can also facilitateseamless transitions between CCM and various levels and conditions ofDCM.

The techniques described herein enable the application of current sourcerectifiers with conventional silicon-based devices without paying thepenalty in efficiency because there is no need to avoid DCM operation.These techniques may also open up more opportunity for current sourcerectifier applications at higher power levels because the penalty of alarge DC link inductance can be avoided. The techniques described hereininclude DBCI PWM control for the current source rectifier that enablesoperation with a lower switching frequency to achieve higher efficiencyand a lower DC link inductance value to achieve smaller size and higherpower density because DCM operation is handled without the side effectsof input current distortion or loss of voltage control. These techniquescan dynamically select the turn-on times for the electricalsemiconductor switches in a current source rectifier such that a propervolt-seconds balance across DC link inductor L_(p) can be maintained.

At least certain embodiments include a new control method for thecurrent source rectifier that can determine the appropriate amount oftime two of the three line-to-line input voltages are applied to theinput side of the current source rectifier depending upon: (1) whetherthe DC link current will become discontinuous before the next switchcycle; and (2) whether one or more of the two applied input voltages isgreater than, equal to, or less than the output voltage. Dead-beatcontrols, by definition, utilize the calculated voltage drop across theDC link inductor L_(p) in order to decide upon the optimal time forpulsed control voltages to be applied across L_(p). Current injectionrefers to the fact that current pulses injected into the current sourcerectifier during a PWM commutation are controlled to achieve a desiredaverage input current. These techniques include a method for detectingwhether the current source rectifier is in CCM or DCM and then forswitching between the calculations for the on-time of active switches ofthe current source rectifier.

FIG. 3A depicts an example block diagram of a controller for a currentsource rectifier according to one embodiment. At any instant of time,the current source rectifier has two or three PWM controlled switches,one switch held on and either two or three switches held off (dependingon whether or not a freewheeling diode is present to provide a path forthe current from the DC link inductor L_(p). If there is no freewheelingdiode then the current source rectifier will commutate between the threeswitch states shown in FIGS. 4-6 below. If there is a freewheeling diodethen the switch state of FIG. 6 is not used and the freewheeling diodeprovides the path for current during the zero state.

In the illustrated embodiment of FIG. 3A, controller 301 for the currentsource rectifier (not shown) includes feed-forward controls 320,feedback controls 324, a line synchronization unit 328, a digital filter334, a DCM detection unit 336, a conventional CCM duty cycle calculationunit 330, and a DBCI duty cycle calculation unit 331. The controller 301further includes output drivers 340 and 342 to provide the signal pulsesto the current source rectifier in accordance with the calculated dutycycles.

Controller 301 includes a DCM detection unit 336 adapted to determinewhen the current source rectifier enters DCM and to adjust thecalculations of the duty cycles accordingly. DCM detection unit 336provides a signal along line 350 that selects between CCM and DCMoperation based on whether DCM is detected. During CCM operation, theCCM inputs to drivers 340 and 342 is selected and the conventional CCMduty cycle calculation unit 330 provides the duty cycles d_(k) _(—) CCMand d_(n) _(—) CCM according to the prior art discussion above. DuringDCM, the DCM inputs to drivers 340 and 342 is selected and the DBCI dutycycle calculation unit 331 provides the duty cycles d_(k) _(—) DCM andd_(n) _(—) DCM according to the techniques described herein. Oneembodiment of the internal components of the DCM detection unit 336 isshown in FIG. 3B.

FIG. 3B depicts an example block diagram of a discontinuous modedetection unit of a controller for a current source rectifier accordingto one embodiment. In the illustrated embodiment, DCM detection unit 336includes a 2nd order digital filter 334 to receive the DC link currenti_(p) and provide a time-averaged version of the DC link current signal<i_(p)>, which is used by calculation units 346 and 348 (along withother inputs vo, vn, vk, and d_(k) _(—) CCM and d_(n) _(—) CCM) todetermine when the current source rectifier enters DCM. An “OR” gate 355is provided such that if either condition is true in calculation units346 and 348, DCM is detected and a signal is provided on the output ofthe detection unit 336.

In order to understand how the current source rectifier is controlled,consider the phasor diagram in FIG. 7, which divides the electricalcycle of the incoming three-phase voltages and currents θ_(i) into sixequal 60 degree sectors. As can be seen, the current source rectifierswitch states have been superimposed on the abc phase plane of thephasor diagram. Three (or four) active switches of the current sourcerectifier and the two applied line-to-line voltages or three appliedline-to-neutral voltages change every 60 degree sector. S_(k) and S_(n)denote the two PWM-controlled switches, S_(q) denotes the switch that isheld on, and S_(z) denotes the switch for the zero state (if used). Forconventional current source rectifiers, three-phase input currents aretypically synthesized by controlling the amount of time PWM-controlledswitches S_(k) and S_(n) are turned on over a switching frequency periodaccording to equations 1-3 below, where the duty cycles are given byequations 4-6.T _(k) =d _(k)(φ_(i))·T _(si)  1T _(n) =d _(n)(φ_(i))·T _(si)  2T _(o)=[1−d _(k)(φ_(i))−d _(n)(φ_(i))]·T _(si)  3where

$\begin{matrix}{{d_{k}\left( \varphi_{i} \right)} = {m_{i} \cdot {\sin\left( {\frac{\pi}{3} - \varphi_{i}} \right)}}} & 4\end{matrix}$d _(n)(φ_(i))=m _(i)·sin(φ_(i))  5

$\begin{matrix}{T_{si} = \frac{1}{f_{si}}} & 6\end{matrix}$The angle φ_(i) is related to θ_(i) by the following relationship:

$\begin{matrix}{{\varphi_{i}(t)} = {{\int{{\omega_{i}(t)} \cdot \ {\mathbb{d}t}}} + \frac{\pi}{6}}} & 7\end{matrix}$where φ_(i) resets to zero at

$\begin{matrix}{{\theta_{i} = \frac{\pi}{6}},\frac{\pi}{2},\frac{5 \cdot \pi}{6},\frac{7 \cdot \pi}{6},\frac{3 \cdot \pi}{2},\frac{11 \cdot \pi}{6}} & 8\end{matrix}$and each of the above values of θ_(i) represents entry into a subsequent60 degree sector and exit from a previous 60 degree sector.

One way to control the current source rectifier is to compare the dutycycles of equations 4 and 5 to symmetrical triangle waves that vary withthe switching frequency f_(si) and are 180 degrees out of phase witheach other in order to produce the gating signals for the PWM-controlledswitches S_(k) and S_(n). Switching functions h_(k) and h_(n) resultfrom a comparison between duty cycles d_(k) and d_(n), respectively, andthe two triangle waves 180 degrees out of phase with each other. Whenh_(k)/h_(n) is high, switch S_(k)/S_(n) is turned on and whenh_(k)/h_(n) is low switch S_(k)/S_(n) is turned off. FIG. 3C depicts agraph demonstrating h_(k), h_(n), i_(p), and <i_(p)> for the currentsource rectifier operating in CCM according to one embodiment. Table 1below shows how the switches of FIG. 1A are assigned in each sector.Those switch states that are generated through comparison with 180degree phase-shifted triangles are designated by the shaded cells underthe S_(k) and S_(n) headings for each sector.

TABLE 1 Pole voltages and currents in each sector

As discussed above, a current source with a freewheeling diode does notrequire the switching of S_(z) in order to create the zero state.Instead, the freewheeling diode automatically creates the zero state byproviding a path through which DC link inductor current can flow whenthe devices are switched off.

PWM operation of the current source rectifier can be understood byrestricting the analysis to a single 60° sector. FIGS. 4-6 show thecurrent source rectifier circuit 110 of FIG. 1A during its threecommutation stages for a single sector (Sector 2) with its two activeswitch states (FIGS. 4 and 5) and the zero or null state (FIG. 6). Thetwo active switch states are named for the active switch, denoted aseither the ‘k’ switch or the ‘n’ switch. The sector is named for theswitch that is held on, the ‘q’ switch. The zero state is produced byswitching on the ‘z’ switch. This ‘k-n-q-z’ convention is followed fromthis point forward in the discussion herein. The ‘k-n-q-z’ switcheschange every sector, as do the input pole voltages (the line-to-linevoltage across the associated input capacitor) designated as v_(k) andv_(n) and the pole currents (the currents that flow through the activeswitch when it is on) designated as v_(k) and v_(n). Table 1 above showsthe pole voltages and currents that are assigned to v_(k), v_(n), i_(k)and in for each sector.

FIGS. 4-6 depict example block diagrams of a current source rectifieroperating in different switch states according to one embodiment. Theassignment of the applied line-to-line voltages v_(k) and v_(n), inputcurrents i_(k) and i_(n), and equivalent line-to-neutral voltages v_(k0)and v_(n0) for each sector is shown in Table 1 above. In a given sector,the current source rectifier PWM-controlled switches (S_(k) and S_(n))and full on switch (S_(q)) connect two AC input voltages to the DC linkinductor L_(p), and synthesize a DC voltage through PWM control that islower than the peak line-to-line voltage of the two voltages. However,depending on when the voltage is connected through S_(k), v_(k), orS_(n), v_(n), the peak input voltage occurs at a different time instantwithin the sector, and, depending on the modulation index m_(i) one ofthe voltages at a given instant within the sector may be lower than theDC output voltage v_(o).

FIG. 4 depicts an example of a current source rectifier in a firstswitch state according to one embodiment. In the illustrated embodiment,this active switch state is referred to as the ‘k’ switch state. In thisstate, the input voltage across the DC link inductor L_(p) is v_(k) andthe current i_(k)=i_(p) flows through L_(p). In order to reach thisstate, switches S_(k) (e.g., S_(i1) from FIG. 1A) and S_(q) are turnedon while the other switches in the current source rectifier remainturned off. FIG. 5 depicts an example of a current source rectifier in asecond switch state according to one embodiment. In the illustratedembodiment, this active switch state is referred to as the ‘n’ switchstate. In this state, the input voltage across the DC link inductorL_(p) is v_(n) and the current i_(n)=i_(p) flows through L_(p). In orderto reach this state, switches S_(n) (e.g., S_(i3) from FIG. 1A) andS_(q) are turned on while the active switches in the current sourcerectifier remain turned off. FIG. 6 depicts an example of a currentsource rectifier in a third switch state according to one embodiment. Inthe illustrated embodiment, this switch state is referred to as the ‘z’or ‘zero’ switch state. In this state, there is no input voltage appliedacross the DC link inductor L_(p) and thus current i_(p) flows to groundand dissipates in the load. In order to reach this state, switches S_(z)(e.g., S_(i5) from FIG. 1A) and S_(q) are turned on while the otheractive switches in the current source rectifier remain turned off.

Different modes of operation exist during one sector depending on theamplitude relationships between v_(k), v_(n) and v_(o). Theidentification of different operating modes has to do with the fact thatunder some conditions, one of the time-varying input voltages v_(k) orv_(n) is lower than the output voltage v_(o) (boost mode). Therelationships between the two AC input voltages, v_(k) and v_(n), andthe output voltage v_(o) is shown in FIG. 8, which depicts an examplegraph of input-to-output voltage ratios of the current source rectifieraccording to one embodiment. The current source rectifier may beconsidered to operate in one of the following voltage ratio modes:

A. buck-buck mode: v_(k)≧v_(o)

v_(n)≧v_(o) with three sub-modes:

-   -   a. v_(k)>v_(n)    -   b. v_(k)=v_(n)    -   c. v_(k)<v_(n)

B. buck-boost mode: v_(k)>v_(o)

v_(n)<v_(o)

C. buck-equal mode: v_(k)>v_(o)

v_(n)=v_(o)

D. equal-equal mode: v_(k)>v_(o)

v_(n)>v_(o)

E. boost-buck mode: v_(k)<v_(o)

v_(n)>v_(o)

F. equal-buck mode: v_(k)=v_(o)

v_(n)>v_(o)

The letters A-F assigned to the voltage ratio modes above are importantand will be described in more detail below. As long as the currentsource rectifier is operating in CCM with the duty cycles of equations 4and 5 applied to switches S_(k) and S_(n), the fact that there aredifferent voltage ratio modes can be ignored by the controller and thefollowing linear relationship occurs between the output voltage v_(o)and magnitude of the line-to-line input voltages V_(i):

$\begin{matrix}{m_{i} = {\frac{2}{\sqrt{3}} \cdot \frac{v_{o}}{V_{i}}}} & 9\end{matrix}$

However, as the load is reduced, the current source rectifier willoperate in DCM and the output voltages result for three representativevalues of m_(i): one that should result in buck-buck modes(m_(i)=0.577), one that has all voltage ratio modes (m_(i)=0.817), andone that has only buck-boost, boost-buck, and equal-equal voltage ratiomodes (m_(i)=1.0). As the current source rectifier load is reduced, itoperates in three regions that have distinctive entry and exitcharacteristics. These conduction regions are identified as follows:

-   -   Region 0 (R0), CCM: the current source rectifier is always in        CCM.    -   Region 1 (R1), DCM (asymmetrical), one of the PWM-controlled        switches gates on before the current in the DC link that        resulted from the previous switch commutation going        discontinuous (FIG. 9, graph 902).    -   Region 2 (R2), DCM (symmetrical): DC link current always goes        discontinuous before each subsequent gating on of the        PWM-controlled switches (FIG. 9, graph 901).        The region designations (R0-R2) are important and will be used        as part of the proposed control description.

Embodiments described herein are also configured to detect the voltageratio mode and conduction region for a current source rectifier atdifferent time instants and to switch between different duty cyclecalculations that result in nearly sinusoidal input currents and linearinput-to-output voltage ratio. Embodiments can also generatefeed-forward commands to calculate duty cycles to ensure input currentstrack the desired feed-forward commands. Embodiments are furtherconfigured to use (1) time-averaged or filtered DC link current feedbackmechanisms, (2) switching frequency and DC link inductance parameters,(3) input and output voltage feedback in detecting conduction regions,(4) voltage ratio modes, and (5) calculation of duty cycles.

These embodiments can perform revised calculations for the duty cyclesassociated with the active switches to ensure that the relationshipshold for the time-averaged input currents <i_(k)> and <i_(n)> (orfiltered input currents i_(k)′ and i_(n)′) for the current sourcerectifier. Note that the third input phase current can be either thetime average of the negative sum of i_(k) and i_(n) (<−i_(k)−i_(n)>) orthe negative sum of the filtered currents i_(k)′ and i_(n)′(−i_(k)′−i_(n)′)). These calculations can change depending upon voltageratio modes and conduction region.

If the current source rectifier is operating in CCM, then the voltageratio mode can be automatically taken into account through the use ofequations 4 and 5 above. If balanced, sinusoidal input voltages areassumed then, in a given sector, the line-to-line voltages used by thecircuits of FIGS. 4-6 can be calculated as follows:v _(k)(φ_(i))=V _(i)·cos(φ_(i))  10

$\begin{matrix}{{v_{n}\left( \varphi_{i} \right)} = {V_{i} \cdot {\cos\left( {\frac{\pi}{3} - \varphi_{i}} \right)}}} & 11\end{matrix}$where V_(i) is the measured peak of the line-to-line voltage on any ofthe three-phase inputs. Two independent line-to-neutral voltages can beshown to be given by the following expressions:

$\begin{matrix}{{v_{k\; 0}\left( \varphi_{i} \right)} = \frac{{2 \cdot {v_{k}\left( \varphi_{i} \right)}} - {v_{n}\left( \varphi_{i} \right)}}{3}} & 12 \\{{v_{n\; 0}\left( \varphi_{i} \right)} = \frac{{2 \cdot {v_{n}\left( \varphi_{i} \right)}} - {v_{k}\left( \varphi_{i} \right)}}{3}} & 13\end{matrix}$where the third line-to-neutral voltage is simply the negative sum ofthe above two voltages. Substituting equations 10 and 11 results in thefollowing expressions for equivalent applied line-to-neutral voltages:

$\begin{matrix}{{v_{k\; 0}\left( \varphi_{i} \right)} = {\frac{V_{i}}{\sqrt{3}} \cdot {\sin\left( {\frac{\pi}{3} - \varphi_{i}} \right)}}} & 14 \\{{v_{n\; 0}\left( \varphi_{i} \right)} = {\frac{V_{i}}{\sqrt{3}} \cdot {\sin\left( \varphi_{i} \right)}}} & 15\end{matrix}$If unity input power factor is desired (which is usually the case), thenthe desired time-averaged or filtered input currents should ideally bein phase with v_(k0) and vn₀ and have the following forms:

$\begin{matrix}{{\left( i_{k} \right)\left( \varphi_{i} \right)} = {I_{i} \cdot {\sin\left( {\frac{\pi}{3} - \varphi_{i}} \right)}}} & 16\end{matrix}$<i _(n)>(φ_(i))=I _(i)·sin(φ_(i))  17

where I_(i) is the fundamental peak phase current of the input current.Note the similarity between equations 16 and 17 with equations 4 and 5.

When the current source rectifier is operating in CCM, then the dutycycles of equations 4 and 5 can be used instead of DBCI-based dutycycles. Under this same condition, the input currents are related to theDC link current by the following relationships:

$\begin{matrix}{\left( i_{k} \right) = {m_{i} \cdot \left\langle i_{p} \right\rangle \cdot {\sin\left( {\frac{\pi}{3} - \varphi_{i}} \right)}}} & 18\end{matrix}$<i _(n)>(φ_(i))=m _(i)·<i _(p)>·sin(φ_(i))  19

When the current source rectifier operates in DCM or CCM withsignificant DC link ripple currents, the objective of the DBCI-PWMcontrol is to ensure that the following relationship holds:

$\begin{matrix}{{i_{x}^{\prime}\left( \varphi_{i} \right)} = {\left\langle {i_{x}\left( \varphi_{i} \right)} \right\rangle = {\frac{v_{x\; 0}^{\prime}\left( \varphi_{i} \right)}{Z_{i} \cdot {\cos\left( \phi_{i} \right)}} = \frac{v_{x\; 0}^{\prime}\left( \varphi_{i} \right)}{Z_{i} \cdot {DPF}}}}} & 20\end{matrix}$where x=k or n and the displacement power factor is DPF orDPF=cos(θ_(i)).

The goal is to ensure that the time average of the pulsed input currentsto the current source rectifier consist mostly of fundamental frequencycomponents only sinusoidally varying quantities with amplitudes that areproportional to the equivalent line-to-neutral voltages. New duty cyclesare derived by solving for duty cycle expressions in terms of thedesired time-averaged (or filtered) input current. These duty cycles arefunctions of the DC link inductance L_(p), the sector angle φ_(i), thetwo applied input voltages v_(k) and v_(n), and the user-selected outputvoltage v_(o)*.

Different duty cycle functions can be preprogrammed into the controllerdepending upon the voltage ratio mode and conduction regions describedabove. The duty cycle expressions are found by solving for duty cyclegiven a set of independent equations as described below:

-   -   Symmetrical DCM, v_(k)>v_(o) and v_(n)>v_(o): time-averaged        current in terms of peak current (di/dt times T_(x), where x=k        or n).    -   Symmetrical DCM, v_(k)<v_(o) or v_(n)<v_(o): time-averaged        current in terms of peak current (di/dt times T_(x), where x=k        or n) and volt-second balance over the switching period.    -   Asymmetrical DCM: time-averaged current in terms of peak current        (di/dt times T_(x), where x=k or n), volt-second balance over        the switching period and estimated DC link current at the end of        the half switching periods.    -   CCM: time-averaged current in terms of peak current (di/dt times        T_(x), where x=k or n), volt-second balance over the switching        period, estimated DC link current at the end of the half        switching periods and time-averaged DC link current in terms of        peak currents (di/dt times T_(x), where x=k and n).

CCM requires either an estimate of the load (from a feed-forwardcommand) or a measurement of the load. The other cases require noknowledge of the load for calculation. As an example of the abovedescribed expressions for duty cycle for the DBCI-PWM technique,consider symmetrical DCM operation with v_(k)>v_(o) and v_(n)>v_(o) orbuck-buck mode. For the purposes of duty cycle selection by the control,the duty cycle expressions are referred to as d_(k) _(—) _(syn) andd_(n) _(—) _(sym). These duty cycle expressions will have the followingforms:

$\begin{matrix}{{d_{k_{sym}}\left( \varphi_{i} \right)} = \sqrt{\frac{2 \cdot L_{p} \cdot f_{si} \cdot \left\langle {i_{k}\left( \varphi_{i} \right)} \right\rangle^{*}}{\left\lbrack {{v_{k}\left( \varphi_{i} \right)} - v_{o}^{*}} \right\rbrack}}} & 21 \\{{d_{n_{sym}}\left( \varphi_{i} \right)} = \sqrt{\frac{2 \cdot L_{p} \cdot f_{si} \cdot \left\langle {i_{n}\left( \varphi_{i} \right)} \right\rangle^{*}}{\left\lbrack {{v_{n}\left( \varphi_{i} \right)} - v_{o}^{*}} \right\rbrack}}} & 22\end{matrix}$

As another example, consider symmetrical DCM operation with v_(n)<v_(o)and v_(k)>v_(o) or buck-boost mode. These duty cycle expressions willhave the following forms:

$\begin{matrix}{{d_{k_{sym}}\left( \varphi_{i} \right)} = \sqrt{\frac{2 \cdot L_{p} \cdot f_{si} \cdot \left\langle {i_{k}\left( \varphi_{i} \right)} \right\rangle^{*}}{\left\lbrack {{v_{k}\left( \varphi_{i} \right)} - v_{o}^{*}} \right\rbrack}}} & 23 \\{{d_{n_{sym}}\left( \varphi_{i} \right)} = \frac{v_{o}^{*} - {2 \cdot {v_{k}\left( \varphi_{i} \right)} \cdot {d_{k_{sym}}\left( \varphi_{i} \right)}}}{2 \cdot \left\lbrack {v_{o}^{*} - {v_{n}\left( \varphi_{i} \right)}} \right\rbrack}} & 24\end{matrix}$

In equations 21-24, the angle φ_(i) and, subsequently, v_(k) and v_(n),are derived from the measured line-to-line input voltages through a linesynchronization algorithm 328 as shown in FIG. 3A. The quantity v_(o)*is the user-selected output voltage. The parameters L_(p) and f_(si) canbe pre-programmed variables and match the physics and implementation ofthe converter circuit.

Embodiments are further configured to detect when the current sourcerectifier is operating in DCM as opposed to CCM. This can beaccomplished by utilizing the DC link current feedback i_(p) andtime-averaging this feedback <i_(p)>. The time-averaged DC link currentfeedback is then compared against the calculated expressions for onehalf of the peak DC link current under DCM operation as shown in FIG.3B. In these expressions, d_(k) and d_(n) are from equations 4 and 5.DCM operation is simply determined by checking to see if the averaged DClink current is less than one-half of the peak of the ripple current. Ifit is, then the current source rectifier is operating in DCM. However,the techniques described herein are not limited to any particular methodfor detecting when the current source rectifier is operating in DCM asmany alternative techniques can be used. For instance, an integratorimplemented in an analog or FPGA circuit can also be used.

Embodiments also provide a provision for determining whether the DCM issymmetric or asymmetric once DCM operation has been detected. AsymmetricDCM occurs if the current in the DC link fails to go discontinuousduring either a freewheeling state or a user-selected state (i.e.buck-boost or boost-buck mode) before the next commanded switch state.Determination of asymmetric DCM requires an estimation of freewheelingor on-times under DCM conditions. For example, in buck-buck mode,asymmetric DCM occurs when the following occurs:

$\begin{matrix}{d_{ok} > \frac{d_{o}}{2}} & 25\end{matrix}$whered _(o)=1−d _(k) −d _(n)  26and

$\begin{matrix}{d_{ok} = \frac{L_{p} \cdot f_{si}}{v_{o}^{*}}} & 27\end{matrix}$

At least certain embodiments address how the time-averaged currentcommands >i_(k)>* and <i_(n)>* in equations 21-24 are calculated. If thephysics of the load is known by the controller, then:

$\begin{matrix}{\left\langle {i_{k}\left( \varphi_{i} \right)} \right\rangle^{*} = {\left\langle i_{p} \right\rangle^{*} \cdot m_{i} \cdot {\sin\left( {\frac{\pi}{3} - \varphi_{i}} \right)}}} & 28\end{matrix}$<i _(n)(φ_(i))>*=<î _(p)>*·m _(i)·sin(φ_(i))  29

where <i_(p)>* is derived from a feed-forward expression of output powerp_(o)*, divided by the user-selected output voltage v_(o)*. If thevoltage controller uses feedback controls, then <i_(p)>* is notnecessary and the time-averaged current commands become:

$\begin{matrix}{\left\langle {i_{k}\left( \varphi_{i} \right)} \right\rangle^{*} = {{\left( {{I_{b} \cdot \Delta}\; m_{i}} \right) \cdot \Delta}\;{m_{i} \cdot {\sin\left( {\frac{\pi}{3} - \varphi_{i}} \right)}}}} & 30\end{matrix}$<i _(n)(φ_(i))>*=(I _(b) ·Δm _(i))·Δm _(i)·sin(φ_(i))  31

where Δm_(i) can be the output of a Proportional Plus Integralregulator. If there is no feed-forward available in the controller, thenthe time-averaged input current commands only require Δm_(i) because itreflects the averaged DC link current <i_(p)>* as needed by the load inorder to maintain the actual output voltage v_(o) equal to theuser-selected output voltage v_(o)*.

FIG. 9 depicts example graphs of the DC link current of the currentsource rectifier during symmetrical and asymmetrical discontinuous modeoperation according to one embodiment. FIG. 9 shows the current sourcerectifier variables zoomed in over one switching period at a pointbetween φ_(i)=0 and φ_(i)=π/6 (assuming positive sequence) operating inbuck-buck symmetric DCM. The most straightforward example is when thecurrent source rectifier is operating in buck-buck symmetrical DCM asshown in graph 901 of FIG. 9. The circuit is operating in buck-buck modewhen v_(k)>v_(o) and v_(n)>v_(o) (see FIG. 8). When m_(i)<0.577 thecurrent source rectifier operates in the buck-buck voltage moderegardless of the position of φ_(i). Symmetric DCM is characterized bythe fact that the DC link inductor current freewheels down to zero (goesdiscontinuous) before each subsequent switching event.

Graph 902 of FIG. 9 shows the current source rectifier variables inbuck-buck asymmetrical DCM. DCM is characterized by the fact that asubsequent switching event occurs when the DC link current hasfreewheeled completely to zero in a half switching period in the ‘z’state associated with the turn-off of either S_(k) or S_(n). Thiscondition can occur as the load has increased from the operating loadwhere the current source rectifier is operating in buck-buck symmetricalDCM, or it may occur at the same operating load as buck-buck symmetricalDCM, but when the switching frequency f_(si) is increased or theinductance L_(p) is reduced. The condition of asymmetrical DCM within agiven half switching period can be determined independently of thesubsequent switching period.

FIG. 10 depicts an example flow chart of a process for controlling acurrent source rectifier according to one embodiment. The current sourcerectifier controller of this disclosure is configured to transitioningbetween continuous and discontinuous modes of operation based ondetecting when the DC link current is continuous or discontinuous. Inthe illustrated embodiment, process 1000 begins at operation 1001wherein the DC link current of the current source rectifier becomesdiscontinuous during operation. The controller then transitions thecurrent source rectifier to a mode of operation based on whether the DClink current is continuous or discontinuous (operation 1002).

Once in DCM, the controller calculates the duty cycles for the currentsource rectifier accordingly (operation 1003). In one embodiment, DCM isdetected when a feedback signal from DC link current through the DC linkinductor of the current source rectifier becomes less than one-half ofthe peak ripple current on the input of the current source rectifier. InDCM, the duty cycles are calculated in DCM based on the input-to-outputvoltage ratios. The duty cycles are calculated differently depending onwhether one or more input voltages applied to the current sourcerectifier are greater than, equal to, or less than output voltage of thecurrent source rectifier. These are referred to herein as the voltageratio modes A-F discussed above.

In the preferred embodiment, in DCM, the duty cycles are furthercalculated based on whether the current source rectifier is operating inthe symmetric or asymmetric conduction region. The asymmetric conductionregion occurs when DC link current through the DC link inductor of thecurrent source rectifier becomes discontinuous after a next duty cycle(or switching period) has already begun. The symmetric conductionregion, on the other hand, occurs when the DC link current becomesdiscontinuous before the next duty cycle. These are referred to hereincollectively as the conduction regions R0-R2 discussed above.

Process 1000 continues at operation 1004 where the controller outputelectrical control signals to turn on one or more of the activeelectrical switches in the current source rectifier based on thecalculated duty cycles. Controlling the active switches in the currentsource rectifier in this manner enables the input currents of thecurrent source rectifier to approximate sinusoidal input currents duringboth the continuous and discontinuous modes of operation. In thepreferred embodiment, the turn-on times for the electrical switches inthe current source rectifier are determined for every 60-degree sectorof an electrical cycle as depicted in the phasor diagram of FIG. 8.

Embodiments are further configured to address the use of DC linkcurrent, time-averaged DC link current or real-time estimates of DC linkcurrent, not only for the determination of DCM operation versus CCMoperation, but also in the determination for expressions for duty cyclesin asymmetric DCM operation. The full implementation of the techniquesdescribed herein results in both approximated sinusoidal input currentsand linear input-to-output voltage ratios. Some typical results can beseen in FIG. 11. These results should be compared to the results fromconventional systems as shown in FIG. 2. For instance, the outputvoltage graph 1101 of FIG. 11 shows little or no overshoot of the outputvoltage at turn-on time. In addition, graphs 1102 show that thetime-averaged input current <i_(k)> closely approximates a sinusoidalsignal.

Throughout the foregoing description, for the purposes of explanation,numerous specific details were set forth in order to provide a thoroughunderstanding of the invention. It will be apparent, however, to personsskilled in the art that these embodiments may be practiced without someof these specific details. Accordingly, the scope and spirit of theinvention should be judged in terms of the claims which follow as wellas the legal equivalents thereof.

What is claimed is:
 1. A controller for a current source rectifier,comprising: a discontinuous mode detection unit configured to determinewhen DC link current of the current source rectifier becomesdiscontinuous; a duty cycle calculation unit adapted to calculate dutycycles for the current source rectifier for operation in a continuous ordiscontinuous mode based on whether the DC link current is continuous ordiscontinuous; a plurality of drivers coupled with the duty cyclecalculation unit to output electrical control signals to turn on one ormore electrical switches in the current source rectifier based on thecalculated duty cycles, wherein time periods the electrical switches areturned on are determined by the calculated duty cycles, wherein thecontroller is adapted to transition to a mode of operation to provide aninput current that approximates a sinusoidal input current during boththe continuous and discontinuous modes of operation.
 2. The controllerof claim 1, wherein the mode of operation is a dead-beat currentinjection (“DBCI”) pulse width modulation (“PWM”) mode of operation. 3.The controller of claim 1, wherein the duty cycle is calculateddifferently when the current source rectifier is operating in continuousor discontinuous modes.
 4. The controller of claim 1, wherein thediscontinuous mode detection unit is configured to detect when thecurrent source rectifier is operating in discontinuous mode bydetermining when a feedback signal from DC link current through aninductor of the current source rectifier is less than one-half of thepeak ripple current on the input of the current source rectifier.
 5. Thecontroller of claim 4, wherein duty cycles in discontinuous mode arecalculated based on input-to-output voltage ratio detected by thediscontinuous mode detection unit, wherein the duty cycles arecalculated differently depending on whether one or more input voltagesapplied to the current source rectifier are greater than, equal to, orless than output voltage of the current source rectifier.
 6. Thecontroller of claim 5, wherein the duty cycles in discontinuous mode arefurther calculated based on whether the current source rectifier isoperating in a symmetric or asymmetric conduction mode, whereinasymmetric conduction mode occurs when DC link current through aninductor of the current source rectifier becomes discontinuous after anext duty cycle.
 7. The controller of claim 6, wherein symmetricconduction mode occurs when the DC link current becomes discontinuousbefore the next duty cycle.
 8. The controller of claim 6, wherein theduty cycle in discontinuous conduction mode during symmetric conductionis proportional to a ratio of the desired input current to theinput-to-output voltage ratio.
 9. The controller of claim 6, wherein theduty cycle in discontinuous conduction mode during asymmetric conductionis proportional to the desired input current multiplied by theinput-to-output voltage ratio.
 10. The controller of claim 1, whereinturn-on times for the electrical switches in the current sourcerectifier are determined for every 60-degree sector of an electricalcycle of input voltages and currents to the current source rectifier.11. The controller of claim 1, wherein the controller is further adaptedto calculate a modulation index for controlling pulse widths of theoutput control signals.
 12. The controller of claim 1 further comprisinga voltage regulator having feedback and feed-forward controls.
 13. Amethod for controlling a current source rectifier comprising:determining when DC link current of the current source rectifier becomesdiscontinuous; calculating duty cycles duty cycles for the currentsource rectifier for operation in a continuous or discontinuous modebased on whether the DC link current is continuous or discontinuous; andproviding output electrical control signals to turn on one or moreelectrical switches in the current source rectifier based on thecalculated duty cycles, wherein time periods the electrical switches areturned on are determined based on the calculated duty cycles, andwherein the controller is adapted to transition to a mode of operationto provide an input current that approximates a sinusoidal input currentduring both the continuous and discontinuous modes of operation.
 14. Themethod of claim 13, wherein the mode of operation is a dead-beat currentinjection (“DBCI”) pulse width modulation (“PWM”) mode of operation. 15.The method of claim 13, wherein the duty cycles are calculateddifferently based on whether the current source rectifier is operatingin continuous or discontinuous mode.
 16. The method of claim 13, whereindiscontinuous mode is detected when a feedback signal from DC linkcurrent through an inductor of the current source rectifier is less thanone-half of the peak ripple current on the input of the current sourcerectifier.
 17. The method of claim 13, further comprising calculatingthe duty cycles in discontinuous mode based on the input-to-outputvoltage ratio, wherein the duty cycles are calculated differentlydepending on whether one or more input voltages applied to the currentsource rectifier are greater than, equal to, or less than output voltageof the current source rectifier.
 18. The method of claim 13, furthercomprising calculating the duty cycles in discontinuous mode based onwhether the current source rectifier is operating in a symmetric orasymmetric conduction mode, wherein asymmetric conduction mode occurswhen DC link current through an inductor of the current source rectifierbecomes discontinuous after a next duty cycle.
 19. The method of claim18, wherein symmetric conduction mode occurs when the DC link currentbecomes discontinuous before the next duty cycle.
 20. The method ofclaim 18, wherein the duty cycle in discontinuous conduction mode duringsymmetric conduction is proportional to a ratio of the desired inputcurrent to the input-to-output voltage ratio.
 21. The method of claim18, wherein the duty cycle in discontinuous conduction mode duringasymmetric conduction is proportional to the desired input currentmultiplied by the input-to-output voltage ratio.
 22. The method of claim13, further comprising determining turn-on times for the electricalswitches in the current source rectifier for every 60-degree sector ofan electrical cycle of input voltages and currents to the current sourcerectifier.
 23. The method of claim 13, further comprising calculating amodulation index for controlling pulse widths of output control signals.